He is referring to Area of Effect. So for example you have an explosion:
Soviet Mortar stats
Let's say the mortar shell lands somewhere and causes an explosion. Its Area Effect Near Distance is 1.5 and the Damage Near multiplier is 1.0. So inside a circle of the radius 1.5 the explosion deals 100% of the mortar shell's damage, so 80 damage if the target is inside.
Its "Distance Far" is 3.0 and the damage multiplier for "far" is 0.25. So if the target is standing exactly 3 from the explosion's center, (and if hit), it takes 25% of the mortar's damage, 20.
Actually it even takes those 25% damage if it is farther away than the distance of 3 because the third zone, (Area Radius) is 6. So a unit between 3 and 6 from the center can take 20 damage.
Between "Far" (3.0) and "Near" (1.5) it scales in a linear manner. You can see this at the top of the page I linked: The blue damage line is at a high level (100%) until it reaches a distance of 1.5, then drops linear until it is at 25% at 3.0 and then stays at 25% all the way out to 6.
The same counts for the explosion's accuracy: It has a "Near" accuracy of 5 and a "Far" accuracy of 0.6. So between "Near distance (1.5)" and "Far distance (3.0)" the accuracy of the explosion decreases but inside the Near circle and in the ring between 3 and 6 distance units, it is constant.
This means that if the target is between 3 to 6 distance units from the explosion's center, the explosion has a chance of only 60% to deal damage at all. This is why sometimes some units don't take damage despite being "closer" to the explosion and some "farther" away still take damage. It is just random.
The "accuracy/damage scaling" is basically just a linear interpolation:
http://en.wikipedia.org/wiki/Linear_interpolation
This can be applied to most stats (accuracy, splash damage, cooldown multipliers) in the game, from the accuracy of small arms to the biggest explosions.